P-1 The Real Number System

Real Numbers—

Irrational Numbers—

the real number that can not be written as the ratio of two

integers.

Rational Numbers—the real number that can be

written as the ration p/q. They either terminate or repeat a

sequence of digits indefinitely

Non-integer fractions the

(positive & negative) Integers—# line

-3, -2. -1, 0, 1, 2, 3,

Whole numbers 0, 1, 2, 3,

Negative Integers -3, -2. -1,

Natural Numbers 1, 2, 3

Zero

Number Lines

0

-OriginNegative NumbersPositive Numbers

Coordinates

Absolute Value• The magnitude of a number or distance

from zero (disregarding the sign)

• |a| = { a if a 0

-a if a ≤ 0

• Properties |a| 0 |-a| = |a| |ab| = |a| |b| a = |a|

b |b|

• Distance on a number line|b-a| = |a-b|

Interpreting Inequalities

• <,>, , ≤

• Describe x ≤ 2

-2 ≤ x < 3

• Inequalities can be used to describe subsets of Real numbers called intervals.

Algebraic Expressions

• 5x, 2x – 3, 4/(x2 + 2)– Collection of variables and constants using +,

- *, ÷– Variable terms– Constants– Coefficients– Evaluate

Bounded IntervalsHave endpoints; finite length

Notation Type Inequality Graph

[a,b]

(a, b)

[a, b)

(a, b]

Closed

Open

Half

Half

a ≤ x ≤ b

a < x< b

a ≤ x < b

a < x ≤ b

a b [ ]

a b ( )

a b ( ]

a b [ )

Unbound IntervalsHave infinite length

Notation Type Inequality Graph

[a,∞)

(a, ∞)

(-∞, b]

(-∞, b)

Half

Open

Half

Open

x a

x > a

x ≤ b

x < b

a b [

a b (

a b )

a b ]

(-∞, ∞ ) Open -∞<x<∞